'I'd give all of Baudelaire for an Olympic swimmer," Céline insisted. It's a provocative statement, typical of Louis-Ferdinand Destouches, who used the nom de plume of Céline. Doctor, linguist, shagger of showgirls and noted antisemite, Céline is now widely acknowledged as the greatest French prose stylist of the 20th century, despite, or perhaps partly because of, the controversy that still dogs the man and his work.

I have French friends who point-blank refuse to read Céline because of the antisemitism, but there is a strong tradition in France of not just indulging, but almost demanding bad behaviour and outrage from its writers (I refer you to Houellebecq, Gide, Cocteau, Colette, Genet and Baudelaire). It tells you a lot about France, in terms of both literature and politics, that after disgracing himself during the Hitler years, Céline was back on the shelves in 1949.

Céline has always had a loyal if small, following in the US with the beats and other beardy counterculture intellectuals (they like to skip over the Jew-bashing, but hey, Ezra Pound got away with it too).

His popularity was based on two opposing elements in his work. The often colloquial, coarse and simple vocabulary he employed (his man-of-the-people credentials, the telling-it-like-it-is, although Céline also has a Captain Haddock-like talent for recherché invective) is heightened by the absence of long, aristocratic, Proustian sentences. But the straightforward language is coupled, especially in the mid-period work, with a modernist disdain for clear exposition and holding the loathsome bourgeois reader's hand. So, boosted by his antiwar spleen and snarling at authority, Céline pulls off the trick of being Henry Miller, John Steinbeck and James Joyce all at the same time.

In Guignol's Band and its sequel London Bridge, you really have to pay close attention to the action to know exactly what's going on, although it's the ride with language that you're paying for – what the French critics often refer to as Céline's "délire".

Journey to the End of Night is Céline's first novel. Published in 1932, it made him an instant literary star. With typical immodesty, Céline felt he was robbed of the Prix Goncourt (won by the now obscure Guy Mazeline) but it didn't matter. Trotsky, Jean-Paul Sartre and Simone de Beauvoir were fans (how the left loved him then).

Journey to the End of Night is the most novel-like of Céline's writings. It has a huge scope, full of pent-up experience and dark lyricism, starting off with the first world war (where Céline served as a professional soldier), encompassing the French African colonies and the industrial might of Detroit (again drawing on the author's own travels). It's like All Quiet on the Western Front, Heart of Darkness and The Grapes of Wrath squeezed into one budget edition. All this is served up with Céline's wit and cynicism, although his characteristic slangy style isn't operating at full power, and there is a stab at a plot. The narrator, Ferdinand Bardamu, follows a character called Robinson (a nod to Crusoe), through these locations. It's one of the longest road-trips in literature.

For all the vulgarity and argot present in Journey, the most striking aspect of the book is the energy and industry involved. In some of his later interviews Céline suggested that he wrote for money. There's no doubt that, in common with many individuals with little money, Céline was concerned with cash, but Journey wasn't an attempt to produce a bestseller; it was an attempt to be number one, to take over, to kill everyone else in the room.

The book's triumph is in its tone. Writers had used it before, but I'd maintain that Céline's great contribution to modern literature is the elevation of sarcasm, of a mordant, sneering cynicism (what the French call narquois) to an art form, a tone that would become a staple of late-20th-century writing, through to Johnny Rotten gurning at his audience.

I've never been able to find any evidence for the influence, but JD Salinger studied French and was in France during the time of Journey's success. Maybe it's just synchronicity, but I have this feeling that Holden Caulfield has a fragment of Bardamu in him, although, of course, his disaffection is much kinder and more soulful than Céline's.

Mea Culpa, Céline's denunciation of the Soviet Union after a tour in 1936, cut off most of his support from the left, but it was his "pamphlet" of 1937 that was to do him considerable damage. Always referred to as a pamphlet (overlooking the sense of "lampoon" in French usage), Trifles for a Massacre is in fact a novel-length text, parts of which are some of the weirdest things I've ever read, seemingly predating postmodernism, William Burroughs and the theatre of the absurd, and truly deserving of the title "delirium". It's out there with Finnegans Wake (although two years earlier), and but for the fact it hadn't been synthesised yet, you'd be wondering if Dr Destouches hadn't scored a tab of LSD.

A few of the derogatory swipes against Jews here might be interpreted as a sort of Swiftian satire (Gide apparently thought Céline was joking), but in case the reader was in any doubt we get the hackneyed charges of an international Zionist conspiracy from Hollywood to Moscow again and again, and Céline does actually liken Jews to "bugs", although he states that as individuals he has no problem with them. Publishing an antisemitic harangue in 1937 with the word "Aryan" in the text and "massacre" in the title is a tough one to explain away, especially as he wrote two more similar fulminations.

Was Céline a fascist? Not quite, although his rabid antisemitism (and by extension his anticommunism) made him popular in those circles. Was he a collaborator? He was convicted for it after the war, although with calm hindsight you could argue he wasn't; but many of his associates were collaborators, and he was just standing too close to them. During the war he actually wrote to the Germans asking for help in obtaining tons of paper so his work could be printed (an act of ego comparable to PG Wodehouse taking up the mike for the Boche while interned).

Guignol's Band was published in 1944, and like much of Céline's work revolves around the first world war. Céline was lucky to get out of it early on, receiving a "Blighty one" and being posted to London, where Guignol's Band is set. Curiously, the narrator is also called Ferdinand, and he gives a foreigner's view of wartime London, as the low-life characters he meets in pubs and brothels are seldom English.

It's no surprise that Irvine Welsh is a fan of Céline; if you added a nae or two, some heroin and a sprinkling of four-letters words, Guignol's Band could be his new novel.

Céline's artistic manifesto is promulgated in a preface to Guignol's Band. He announces, among other things, "I annoy everyone" and "Jazz toppled the waltz … you write 'telegraphically' or you don't write at all." Guignol's Band is almost the final stage of Céline's "telegraphic" style, the nearly complete reliance on ellipses and exclamation marks. It's not easy to write a pastiche of Gide, Proust, Giono, Mauriac, Sartre or Camus, but you could teach a six-year-old to do Céline. It's a simple, but highly effective invention.

Guignol's Band assures us that there are some things that never change. "He couldn't be employed," Ferdinand says of a Slav, "and then he really drank too much, even for England." One of the pimps makes the joke that has survived to this day. The weather's not that bad in England: it only rains twice a year … for six months at a time.

London Bridge continues Ferdinand's story as he gets involved with a gas-mask project and an underage girl (preempting Nabokov, although London Bridge didn't get to the bookshops until 1964). Céline's account of a Zeppelin bombing raid is one of the highlights of the book.

Alma's reissued editions rely heavily on past American translations, so some of it may sound odd to British ears, given the British setting. There is also a particular problem with Céline in that he falls very much into the untranslatable bracket; much of his appeal is in the tone and musicality of his language, and its vast register. He needs a translator of genius rather than mere skill.

London Bridge had to wait 20 years to reach the bookshops because Céline chose to decamp with the Vichy government and ended up incarcerated in Denmark for 18 months. He toyed with the idea of doing a third volume of Guignol, but got no further than an outline, which is in the Pléiade edition of his works, the ultimate accolade for a writer in France.

The period on the run and in chokey gave Céline the inspiration for his final great performance, the Château trilogy (and of course, a trilogy without an ounce of repentance – Céline just doesn't do repentance – but rather a lamentation on his persecution).

Here, because, I assume he was revelling in the freedom of not caring about popularity any more, and because the story as such consists of Céline wallowing in himself, along with undramatic incidents and conversations, his style stands naked. Pure style, nothing else.

For me, Céline's best work is at the beginning and the end, Journey to the End of Night and the Château trilogy (he badly needs an editor in both Guignol's Band and London Bridge, which I find a bit meandering and overwritten). Born in the shadow of entrenched realism and naturalism, Céline ripped up the textbook. He wasn't the first French writer to use a colloquial style, but he was the first to use it so relentlessly and powerfully, to create a brand, the rant, whether it was delirious, lyrical or raging. If you read French, his prose is simply mesmerising.

There is a shamelessness and an uncrushability about Céline that many successful writers have (in an Anglo-Saxon context Daniel Defoe and Jeffrey Archer come to mind). Part of Céline's appeal is that you can't imagine him holding back, not saying something for fear of offending. Offending was his business. And he worked for it. If you listen to recordings of his interviews, you hear the rapid, insistent speech of a determined man.

Allegedly, he died on the day in 1961 when he finished his last book, the final Château volume, Rigadoon (where the Jews have been replaced by the Chinese as his chief bugbear), dedicated "To Animals" (behind the nihilist, a softy with a parrot and a cat). In Rigadoon he makes this prediction: "I'm absolutely Pléiade … like La Fontaine, Clément Marot, Du Bellay and Rabelais eh! And Ronsard! … I tell you if I keep a little cool, in two, three centuries I'll be helping people sit the baccalauréat …" He was in the schools 30 years later.